---
title: "Scale and similar shapes"
description: "Solve problems involving similar shapes where the scale factor is known or can be found"
canonical: https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW
source: https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW.md
retrieved: 2026-10-19
---

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# Scale and similar shapes

Solve problems involving similar shapes where the scale factor is known or can be found

Subject: Mathematics · Area: Ratio & Proportion · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW

## Ready when they can

- Find the missing side of a similar rectangle given a scale factor of 3
- Determine the scale factor between two similar triangles from given side lengths
- Use a scale factor to enlarge or reduce a shape and verify that all sides are in the same ratio

## Lesson: Scale and similar shapes

Two shapes are similar when they have the exact same shape but different sizes. Every side on the small shape matches a side on the big shape, and all the matching sides are stretched by the same amount. That amount is called the scale factor.

*(drawing: The big rectangle's side is 3 times the small rectangle's side.)*

**Example.** A small rectangle is 4 cm by 6 cm. It is enlarged with a scale factor of 3. Multiply each side by 3: 4 x 3 = 12 cm and 6 x 3 = 18 cm. The new rectangle is 12 cm by 18 cm, and both sides grew by the same scale factor.

**Tip.** To find a missing side, multiply the small shape's side by the scale factor. To find the scale factor itself, divide a big shape's side by the matching small shape's side.

This works for any similar shapes, including triangles, squares, and other polygons. Just make sure you compare matching sides, the ones in the same position on each shape.

**Recap.** Similar shapes have matching sides in the same ratio, so multiply by the scale factor to enlarge and divide to find it.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Area and perimeter of rectangles](https://lightmysky.com/learn/mathematics/area-and-perimeter-of-rectangles-mt_eiB3-6pu6a)
- [Bar Models for Ratios](https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU)
- [Ratio and proportion vocabulary](https://lightmysky.com/learn/mathematics/ratio-and-proportion-vocabulary-mt_ESgc4YBw-a)
- [Ratio Problems](https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL)
- [Classifying shapes by properties](https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh)

## Opens up

- [Scale drawings and maps](https://lightmysky.com/learn/mathematics/scale-drawings-and-maps-mt_1badik7iKJ)
- [Similarity and enlargement](https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B)
- [Real-World Mathematical Modelling](https://lightmysky.com/learn/mathematics/real-world-mathematical-modelling-mt_yqZiX6vS7D)